Two subset with equal sum
Two subset with equal sum
Given any set of $10$ natural numbers between $1$ and $99$ inclusive, prove that there are two disjoint nonempty subsets of the set with equal sums of their elements.
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 Posts: 3
 Joined: Thu Dec 16, 2010 2:06 pm
Re: Two subset with equal sum
The highest sum of a subset here is 945(=90+91+92+93+94+95+96+97+98+99)
So the sum ranges from 1 to 945.
the number of subset is 1023(=2^101)
1023 subsets,945 sums,pigeonhole,..........................thats it \m/
So the sum ranges from 1 to 945.
the number of subset is 1023(=2^101)
1023 subsets,945 sums,pigeonhole,..........................thats it \m/

 Posts: 3
 Joined: Thu Dec 16, 2010 2:06 pm
Re: Two subset with equal sum
forgot to write......Two set with same sum can have common elements.If they do,substract the sum of common elements from both sets and there will be two disjoint sets with same sum.If they don't,then the case is solved:):)